1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Projectile motion: determine launch angle

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data

    A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s.

    -Determine the angle [itex]\Theta[/itex] required for the projectile to hit the bottom of the hill within one degree.
    -How long does the projectile take to hit the bottom of the hill?
    -There is a target moving at a constant velocity of 20m/s down the hill. How long should you delay firing to hit the target as it reaches the bottom of the hill?
    -Find the maximum distance this projectile can travel as measured from the bottom of the hill.


    2. Relevant equations

    x=x[itex]_{0}[/itex]+v[itex]_{0x}[/itex]t
    v[itex]_{y}[/itex]=v[itex]_{0y}[/itex]t-gt[itex]^{2}[/itex]
    y=y[itex]_{0}[/itex]+v[itex]_{0y}[/itex]t-0.5gt[itex]^{2}[/itex]
    v[itex]^{2}_{y}[/itex]=v[itex]^{2}_{0y}[/itex]-2g(y-y[itex]_{0}[/itex])


    3. The attempt at a solution

    I have tried using all of the two-dimensional kinematics equations with some success but the problem is that [itex]\Theta[/itex] is unknown so I can't find t or v[itex]_{fy}[/itex].

    My best attempts are as so:
    v[itex]_{yf}[/itex]=55sin[itex]\Theta[/itex]-9.81t
    188=55cos([itex]\Theta[/itex])t
    188=0+55cos([itex]\Theta[/itex])t-4.9t[itex]^{2}[/itex]

    The diagram for the problem is attached.
    Either it is algebra more complicated than I am used to or I am missing something very simple. I am confident that if I could solve for [itex]\Theta[/itex] OR t I could finish the problem easily. I can't seem to get a solveable equation. Thank you for your help and I apologize if there are syntax errors as I am a first time user.
     

    Attached Files:

    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 15, 2014 #2
    There is inconsistency , the questions on the attachment and the problem statement you provided . I would like to help you but there are some ambiguity .
     
  4. Jan 15, 2014 #3
    I apologize for that. I just updated the post to match the wording of the diagram exactly. I have continued to work on this problem and used a few pages of paper, but still have not been able to find a way to solve for theta.
     
  5. Jan 15, 2014 #4
    You have to find the range in terms of the initial angle then try to optimize it . That is how I solved it . You have to think why one needs an optimization approach to solve this problem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted